BERND PAPE Asset Allocation, Multivariate Position Based Trading ...

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128 ACTA WASAENSIA0.4Logreturns Asset 10.20−0.2−0.40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 10 4Logreturns Asset 20.40.20−0.2−0.4−0.60 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 10 4Logreturns Equal Weighted Index0.40.20−0.2−0.40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 10 4Logreturns Capitalization Weighted Index0.40.20−0.2−0.40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 10 4Figure 14. Logreturns of the two stocks, the equal weighted index, and the capitalizationweighted index over 20,000 observations.
ACTA WASAENSIA 129Table 16. Summary statistics for the simulated logreturns of the two stocks r 1 and r 2 ,the equal weighted index r EW , and the capitalization weigthed index r CW .Asset Avg. raw Avg. absolute Return Return ReturnReturn×10 −3 Return Variance×10 −3 Skewness KurtosisStock 1 0.0040 0.0180 0.7071 0.0773 12.07Stock 2 -0.0231 0.0179 0.7251 -0.1424 25.88Index (EW) 0.1728 0.0133 0.3514 0.1331 10.47Index (CW) -0.0077 0.0144 0.4886 -0.3443 37.58series are close to symmetric, with average daily absolute returns in the range of 1 to2percent,andanannualvolatilityintherange between 30 and 40 percent. Becausethe individual stock returns are cross-sectionally close to uncorrelated (ρ = −0.0195),the variance of the equal weighted index is about half the variance of the individualstock returns. All time series are heavily leptokurtic with double digit coefficients ofkurtosis. The variance and kurtosis of the capitalization weighted index are somewhathigher than those of the equal weighted index due to their higher weight on the stockwith the larger mispricing and therefore higher probability of large returns.Empirically observed stock returns are in general positively correlated, which is notreplicated by the simulations presented here under the simplifying assumption of equalconstant fundamental values for both stocks. If we had assumed their intrinsic valuesto follow correlated unit root processes, uncorrelatedness in the current setup wouldpresumably have translated into identical correlations of fundamental and trading returns.The model may therefore very well be consistent with the positively correlatedreturns observed in real equity markets, as far as fundamental values are positivelycorrelated. The positive cross-sectional correlation between stocks would just drop outfrom the list of behaviourally explained stylized facts and instead be attributed to economicfacts such as exposure to similiar risk factors etc. In any case, I am not awareof any order-based study, which would have reported cross-sectionally uncorrelated oreven positively correlated return series, as the findings from empirically oberved equityreturns would require.Figures 15 and 16 demonstrate that the outbreaks of volatility in trading returns arerelated to the number of stocks owned by chartists in a similar way as in the simulation
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ACTA WASAENSIA 52.10.1 Cross-Sectio
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ACTA WASAENSIA 7A5 Matlabcodeforerr
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10 ACTA WASAENSIAIn chapter 5 I sha
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12 ACTA WASAENSIA2 Statistical Prop
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14 ACTA WASAENSIA2.2 Absence of Ser
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ACTA WASAENSIA 17The survival or ta
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ACTA WASAENSIA 19& Scheinkman (1987
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ACTA WASAENSIA 212.6 Long Range Dep
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ACTA WASAENSIA 23A particular class
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26 ACTA WASAENSIAMultiscaling may t
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28 ACTA WASAENSIAHansen (1982) to c
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30 ACTA WASAENSIAThe leverage hypot
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32 ACTA WASAENSIAIn order to aviod
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34 ACTA WASAENSIAon a risk-adjusted
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36 ACTA WASAENSIAplanations for the
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38 ACTA WASAENSIAspeculative prices
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40 ACTA WASAENSIAindex α is howeve
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42 ACTA WASAENSIAThis approach has
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44 ACTA WASAENSIAimplying exponenti
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46 ACTA WASAENSIA3.2.4 Descriptive
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48 ACTA WASAENSIAdivisible version
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50 ACTA WASAENSIAto check their ade
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52 ACTA WASAENSIAvolatility into th
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54 ACTA WASAENSIAfeedback of the co
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56 ACTA WASAENSIAarriving at the fo
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58 ACTA WASAENSIAat iteration k com
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60 ACTA WASAENSIAmultipliers in the
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62 ACTA WASAENSIALux & Ausloos (200
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64 ACTA WASAENSIAmarkets dominated
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66 ACTA WASAENSIAThe “representat
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68 ACTA WASAENSIA(1983) 114 motivat
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70 ACTA WASAENSIAIn the following w
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72 ACTA WASAENSIASethi (1996) exten
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74 ACTA WASAENSIASummation over all
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76 ACTA WASAENSIAthe microscopic un
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Page 80 and 81: 80 ACTA WASAENSIAWe wish to obtain
Page 82 and 83: 82 ACTA WASAENSIAindividual markets
Page 84 and 85: 84 ACTA WASAENSIAreturn series. I l
Page 86 and 87: 86 ACTA WASAENSIASwitches between c
Page 88 and 89: 88 ACTA WASAENSIAfollowing necessar
Page 90 and 91: 90 ACTA WASAENSIATable 1. Parameter
Page 92 and 93: 92 ACTA WASAENSIAin stepwise search
Page 94 and 95: 94 ACTA WASAENSIA0.2Logreturns Para
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Page 98 and 99: 98 ACTA WASAENSIATable 3. Kurtosis
Page 100 and 101: 100 ACTA WASAENSIAthe most extreme
Page 102 and 103: 102 ACTA WASAENSIATable 4. Estimate
Page 104 and 105: 104 ACTA WASAENSIATable 8. Results
Page 106 and 107: 106 ACTA WASAENSIATable 9. Results
Page 108 and 109: 108 ACTA WASAENSIATable 11. Paramet
Page 110 and 111: 110 ACTA WASAENSIA1 x 105 Aggr. Inv
Page 112 and 113: 112 ACTA WASAENSIA200Aggr. Inventor
Page 114 and 115: 114 ACTA WASAENSIA5 x 105 Aggr. Wea
Page 116 and 117: 116 ACTA WASAENSIAOverall, we can a
Page 118 and 119: 118 ACTA WASAENSIAby Lux (1998). Th
Page 120 and 121: 120 ACTA WASAENSIAwhere s is a disc
Page 122 and 123: 122 ACTA WASAENSIAprocessing valuat
Page 124 and 125: 124 ACTA WASAENSIAProof. See append
Page 126 and 127: 126 ACTA WASAENSIA2.5Logarithmice T
Page 130 and 131: 130 ACTA WASAENSIA0.4Logreturns Ass
Page 132 and 133: 132 ACTA WASAENSIATable 17. Probabi
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Page 136 and 137: 136 ACTA WASAENSIAIn order to test
Page 138 and 139: 138 ACTA WASAENSIAReferencesAbhyank
Page 140 and 141: 140 ACTA WASAENSIABaillie, R. T. (1
Page 142 and 143: 142 ACTA WASAENSIABlack, F. & M. Sc
Page 144 and 145: 144 ACTA WASAENSIAButler, R. J., J.
Page 146 and 147: 146 ACTA WASAENSIACont, R. (2001).
Page 148 and 149: 148 ACTA WASAENSIAEmbrechts, P., C.
Page 150 and 151: 150 ACTA WASAENSIAFielitz, B. D. (1
Page 152 and 153: 152 ACTA WASAENSIAGhysels, E., A. C
Page 154 and 155: 154 ACTA WASAENSIAHeston, S. L. (19
Page 156 and 157: 156 ACTA WASAENSIAKaldor, N. (1939)
Page 158 and 159: 158 ACTA WASAENSIALiesenfeld, R. (1
Page 160 and 161: 160 ACTA WASAENSIALye, J. N. & V. L
Page 162 and 163: 162 ACTA WASAENSIAMikosch, T. (2003
Page 164 and 165: 164 ACTA WASAENSIAPindyck, R. S. (1
Page 166 and 167: 166 ACTA WASAENSIASethi, R. (1996).
Page 168 and 169: 168 ACTA WASAENSIATesfatsion, L. &
Page 170 and 171: 170 ACTA WASAENSIAAAppendixA1Matlab
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Page 176 and 177: 176 ACTA WASAENSIA275276 figure;277
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178 ACTA WASAENSIA45 end464748 % In
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180 ACTA WASAENSIA454647 % Check wh
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182 ACTA WASAENSIAA4Matlab code for
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184 ACTA WASAENSIA888990 % create P
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186 ACTA WASAENSIA4344 nobs = 500;
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188 ACTA WASAENSIAA6Matlab code for
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190 ACTA WASAENSIA9192 for t = 1:T
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192 ACTA WASAENSIA185 fcash = fcash
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194 ACTA WASAENSIA279280281 %Output
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196 ACTA WASAENSIA(4.20), and o(τ
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198 ACTA WASAENSIAas t = n k P ˙
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200 ACTA WASAENSIA nBn˙f2 = v B n
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202 ACTA WASAENSIA f˙1−c1 = v B
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204 ACTA WASAENSIAlocal stability o
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